Today's view of triality is the $21$ edges of our favourite polytope: the Stasheff associahedron in three dimensions! At each trivalent vertex there is a triplet $(A,B,C)$ of edges. The vertex signs are then defined by the cycling of the letters at the vertex. An arbitrary source and target vertex are marked.

8 years ago

OK, so I believe I counted $21 = 3 \times 7$ correctly, but please check the invariance of letter permutations ...

ReplyDeleteKea,

ReplyDeleteI have seen such structures relating to the shape of cells in some of the five fold analogs to icosahedra and so on. But this is new to me so thanks.

The PeSla